Video: What is Probability in Math? - Definition & Overview

Remember throwing a quarter and calling out heads or tails? Learn what this has to do with probability. Also learn how you can use your newly-learned skills from this lesson to help you decide whether you should play heads or tails at all!2016-08-26

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Remember throwing a quarter and calling out heads or tails? Learn what this has to do with probability. Also learn how you can use your newly-learned skills from this lesson to help you decide whether you should play heads or tails at all!

Definition and Formula

Probability is the likelihood of something happening. When someone tells you the probability of something happening, they are telling you how likely that something is. When people buy lottery tickets, the probability of winning is usually stated, and sometimes, it can be something like 1/10,000,000 (or even worse). This tells you that it is not very likely that you will win.

The formula for probability tells you how many choices you have over the number of possible combinations.

Calculating Probability

To calculate probability, you need to know how many possible options or outcomes there are and how many right combinations you have. Let's calculate the probability of throwing dice to see how it works.

First, we know that a die has a total of 6 possible outcomes. You can roll a 1, 2, 3, 4, 5, or 6. Next, we need to know how many choices we have. Whenever you roll, you will get one of the numbers. You can't roll and get two different numbers with one die. So, our number of choices is 1. Using our formula for probability, we get a probability of 1/6.

Our probability of rolling any of the numbers is 1/6. The probability of rolling a 2 is 1/6, of rolling a 3 is also 1/6, and so on.

Let's try another problem. Let's say we have a grab bag of apples and oranges. We want to find out the probability of picking an apple from the bag. One thing we need to know is the number of apples in the bag because that gives us the number of 'correct' choices, which is the number of our possible choices in the top part of the calculation.

We also need to know the total number of fruits in the bag, for this gives us the total number of choices we have, or the total number of options in the bottom part of the calculation. The person with the grab bag tells us there are 10 apples and 20 oranges in the bag. So, what is our probability of picking an apple? We have 10 apples, one of which we want, and a total of 30 fruits to pick from.

Our probability is 1/3 for picking an apple. If you compare this with our probability of rolling a number on a die, the probability of picking an apple from the grab bag is higher. It is more likely that we will pick an apple than that we will roll a particular number.

In both cases, we can leave the probability in fraction form or we can convert it to decimal form: 1/6 becomes 0.17, and 1/3 becomes 0.33.

Understanding Probability

Our total number of options will always outnumber our possible choices, so probability will always give you a number or fraction between 0 and 1. The closer the number is to 1, the more likely it is to happen. If the probability is 1, then this particular event will always happen. Having a probability of 0 or 1 are the only assured events in probability. Otherwise, things are only as likely as the probability to happen - no guarantees.

The probability of uncertain events, such as rolling a die, only gives you the likelihood of something happening; it doesn't give you certainty. You can't be certain that the event will happen. Even though the odds of rolling a particular number on a die is 1/6, rolling a die 6 times does not guarantee you will roll your number in those 6 times.

There are instances where probability will tell you that you will definitely win if you try so many times. It is when there are only a limited number of combinations that you can pick from. Take the lottery, for example. There are only a limited number of combinations you can pick from. Although that is a large number, if you bought enough tickets so that you could mark every single combination, then you are guaranteed a win because one of your combinations must be picked. So with odds of 1/10,000,000, if you bought 10,000,000 tickets and made sure to include every possible combination of numbers, you are guaranteed that one of them will win.

Lesson Summary

Probability tells you the likelihood of an event happening. The lower the probability, the less likely it is to happen. The higher the probability, the more likely it is to happen. Probability is a number or fraction between 0 and 1. A probability of 1 means something will always happen, and a probability of 0 means something will never happen. Only a probability of 0 or 1 means certainty. All other times, it means the likelihood of it happening - and it does not guarantee whether that something will happen or not. The only case where it does guarantee that something will happen if you try it so many times is in the case of a limited number of combinations - such as the lottery.

Learning Outcomes

Completing this lesson on probability could result in your capacity to:

Provide the definition of probability

Calculate probability

Distinguish between the probability and the certainty of an event occurring

Summary:

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